Further Research On The Exhaustive-Service M/M/1Queueing Model With Single Vacations

This thesis is divided into two chapters. Chapter1is split into two sections. In Section1, we introduce briefly the history of queueing theory. In Section2, we first introduce sup-plementary variable technique, then we state the problem that we will study in this thesis. Chapter2consists of two sections. In Section1, firstly we introduce the exhaustive-service M/M/1queueing model with single vacations, then we convert the model into an abstract Cauchy problem in a Banach space by introducing a state space, operators and their domains, lastly we introduce the main results obtained by other researchers. In Section2, we prove that if λ<η<μ-λ+2(?)λη, then all θ(2(?)λη-λ-η) are eigenvalues of the operator, which corresponds to the M/M/1queueing model with single vacations, with geometric multiplicity one for all θ∈(0,1).